Vol. 128 (2015) ACTA PHYSICA POLONICA A No. 3

Electric Field Modelling in Gas-Insulated Substation

for Analysis of Conditions for Partial Discharge Phenomena

B. Florkowskaa,*, P. Zydro«a and A. Jackowicz-Korczy«skib

aAGH � University of Science and Technology, Department of Electrical and Power Engineering,

al. Mickiewicza 30, 30-059 Kraków, PolandbStator Service Polska, al. Ro¹dzie«skiego 188, 40-203 Katowice, Poland

(Received January 3, 2015; in �nal form August 6, 2015)

The paper refers to diagnostics problems connected with the presence of partial discharges in gas-insulatedsubstation. The basic stimulus for partial discharges generation is local, high value electric �eld, greater than theinception one. The numerical simulations of the electric �eld distribution in the part of the gas insulating systemand in the vicinity of the metallic protrusion located on high voltage conductor are presented. Such defects areoften present in SF6 insulated constructions and are the cause of a local increase of the electric �eld. Theoreticalanalysis of physical mechanism of partial discharges initiation and development in the case of micro-needle typedefects is described.

DOI: 10.12693/APhysPolA.128.319

PACS: 51.50.+v, 52.80.�s, 84.70.+p, 41.20.�q

1. Introduction

Gas-insulated substations (GISs) with sulphur hexa�u-oride (SF6) have been used for many years because of ex-cellent insulating and arc extinguishing properties of SF6.Gas-insulated constructions are used in medium and highvoltage substations. On the basis of many years experi-ence all over the world it has been concluded that reliabil-ity of substations, limited by insulating system dielectricperformance can be treated satisfactory for the arrange-ments up to nominal voltage 170 kV. Currently, the maindevelopment and application of gas insulated substationsconcerns the high- and extra high voltages [1�3]. Dete-rioration of gas due to partial discharge (PD) phenom-ena is the main problem of insulating systems with SF6.The sulphur hexa�uoride practically does not degradein-service at the working electric �eld stress if there areno partial discharges. When SF6 gas is exposed to in-creased electric �eld and partial discharges are present,the gas decomposes into various products, depending onthe discharge energy, water content and purity of gas.The insulation performance of SF6 degrades under inho-mogeneous electric �eld increased mainly under the in-�uence of conducting defects on the conductors or on thesurface of insulators. The danger of partial discharges isreal and has essential meaning for reliable operation ofmodern gas insulated substations. Elimination of partialdischarges from GIS constructions, their preventive de-tection and development of new diagnostics methods aredemanded [4]. The GIS monitoring allowing detectionof the PD signals inside the GIS construction using elec-trical method, conventional and special UHF/VHF have

*corresponding author; e-mail: beflor@agh.edu.pl

evolved [5�13]. The physicochemical methods of GISmonitoring based on, e.g. gas spectroscopy method [14]or application of carbon nanotube gas sensor [15] werealso reported.The gas-insulated substation has a complicated design

and contains elements which di�er substantially in termsof the electric �eld distribution. The GIS design opti-mization refers to the selection of the permissible valueof the electric �eld in the insulating system due to thedielectric strength of SF6, but also thermal and mechan-ical properties of the GIS construction [16]. This condi-tion may not be su�cient in the case of a local increaseof the electric �eld in a gas insulating system, at whichpartial discharges are initiated. Being the basic task atpreliminary stage of new substation project, the analysisof electric �eld distribution in substations modules is thebasis for the recognition and description of conditions ofPD appearance in gas-insulated substations. Deforma-tion of electric �eld and its local increase during normaloperation are usually e�ects of the presence of metallicprotrusion or micro-needles in insulating system of thesubstation [17, 18].The above problem is presented in the article on the

example of a spherical connector, one of the constructionelements of GIS. The electric �eld within the elementwas numerically modelled, both in terms of optimizing itsdesign and with respect to the presence of local defectsleading to the formation of partial discharges.

2. Electric �eld stress distribution within

modules of a gas insulated substation

The photo in Fig. 1 shows a fragment of a gas insulatedmodule containing a speci�c example of GIS structure el-ement, which is a spherical connector. The straight mod-ules with a 90◦ angular module are the so-called L-shapedconnections.

(319)

320 B. Florkowska, P. Zydro«, A. Jackowicz-Korczy«ski

Fig. 1. Spherical connector as a part of 1-phaseL-shaped GIS module.

Spherical connectors are located in aluminium or steeltank with SF6 under the pressure from 0.2 MPa upto 0.5 MPa as the main insulating medium. The model ofthe substation's spherical connector consists of a pair ofcoaxial cylinders radii r, R (Fig. 2, part I) and concentricspheres radii rk, Rk (Fig. 2, part II). The basis of con-nector designing is the calculation of the maximum valueof electric �eld stress Er at the HV conductor surfacewith radius r and electric �eld stress Erk at the sphereradius rk.

Fig. 2. The model of a spherical connector in L-shapedtank, Part I: coaxial cylinders, r � radius of HV con-ductor, R� radius of grounded tank, Part II: concentricspheres radii rk, Rk.

Fig. 3. The electric �eld values at the surface of innercylinder Er = f(R/r) and at the surface of inner sphereErk = f(Rk/rk).

Dimensioning of spherical connector for GIS moduleworking at the rated voltage Un consists in determiningthe radii rk, Rk and R at predetermined permissible valueof the electric �eld Er at the surface of the pipe-type bus-bar (inner cylinder radius r) in the straight portion of theconnector (part I). The dimensions of concentric spheres,i.e. its radii Rk and rk (Fig. 2) should be properly evalu-ated, so the electric �eld stress Er at the surface of innercylinder radius r (conductor) should be equal to the elec-tric �eld Erk at the surface of the inner sphere radius rk(Fig. 3):

Erk min = Er min.

Part I � model of coaxial cylinders

The value of the electric �eld in a coaxial model sys-tem at a voltage of U , in the area r < x < R, accordingto the Gaussian law is

Ex =Q

2πεlx, (1)

where Q/l � charge per unit length, ε � dielectricpermittivity.The electric �eld at the surface of the pipe-type busbar

radius r is equal to

Er =U

r

1

ln(R/r)(2)

and its value depends on the ratio of radii R/r.The lowest value of electric �eld Er min at the rated

voltage takes place for dEr/d(R/r) = 0. Then, the ratioof radii R/r is equal to e constant, i.e. the internal diam-eter 2R of outer cylinder to diameter of the high voltageconductor meets equation 2R = 5.4r (Fig. 3).Part II � model of concentric spheres

The electric �eld in a spherical model system with volt-age U , in the area rk < x < Rk, according to the Gaus-sian law is

Ex =Q

4πεx2. (3)

The electric �eld at the surface of the inner sphere ra-dius rk is

Erk =U

rk· 1

1− (rk/Rk), (4)

so the value of Erk depends on the ratio of radii Rk/rk.The lowest value of the electric �eld stress at

the surface of inner sphere is present when thedErk/d(Rk/rk) = 0. Then, ratio of radii Rk/rk = 2(Fig. 3).The exemplary results of numerically simulated electric

�eld distribution for L-shaped tank model obtained bythe FEM method with the ANSYS software are shown inFigs. 4 and 5.The result of computer simulation for optimal con-

struction of L-shaped tank geometry (Fig. 4) is the elec-tric �eld image (Fig. 5) with uniformly distributed elec-tric �eld stress on the surface of the high voltage conduc-tor and on the spherical connector. Precise numericalmodelling of the GIS module geometry allows for opti-mizing the electric �eld distribution on the surfaces ofthe individual components at the design stage.

Electric Field Modelling in Gas-Insulated Substation. . . 321

Fig. 4. Numerical modelling of spherical connector ge-ometry in L-shape tank.

Fig. 5. The image of the electric �eld stress in optimalmodel of spherical connector.

Software for modelling of electric �elds is thus a pow-erful tool that supports the processes of designing andpreliminary evaluation of the correctness of the project.In every case the �nal veri�cation lies in real HV testsperformed on prototype devices in laboratory conditions.

3. Modelling of electric �eld distribution in the

vicinity of local sources of partial discharges

The maximum values of the electric �eld in sphericalconnectors ensure their normal operation at rated voltagegas insulated substations. This state can be a�ected bydefects in the gas insulated system in its modules whichcause a local increase of the electric �eld. Defects in asubstation module are the sources of partial dischargesin this construction. One can distinguish the `stable' de-fects and the `dynamic' ones, which are free conductiveparticles moving in the gas space or on the surface ofconductive elements and insulators (Fig. 6).Basic kinds of defects are:

1. micro-needle on the high voltage conductor (1′) oron the grounded tank (1′′),

2. free-moving particles in gaseous space with �oatingpotential (2),

3. conductive particles/contaminations on the insula-tor surface (3),

Fig. 6. Part of the single-phase substation module andpossible location of di�erent defects.

4. gaseous inclusion in solid insulation of the spacerinsulating material (4),

5. particles in the �triple point� (5).

Typically, above-mentioned defects have an e�ect onthe electric �eld distribution in the substation module.Moreover, the local electric �eld stress can be higher thanthe partial discharge inception one.Each defect, which can potentially generate discharges,

both during the post-installation tests or during normalworking of substation, can be classi�ed as critical be-cause it results in decrease of withstand voltage belowthe coordination voltage value [19]. This value equalsto the lowest substation withstand voltage value in thedetermined time of its exploitation.Particular hazard in SF6 systems stems from the over-

voltages which can incept discharges and as a resultchange the physical state of the insulating gas.The main aims of the diagnostic system of high voltage

insulation based on partial discharges are:

� detection of partial discharges in the presence ofnoises and disturbances,

� identi�cation and localisation of partial dischargessources linked to GIS defects,

� on-line monitoring and assessment of partial dis-charges in working GIS.

Next follows the analysis of impact of defect type 1(Fig. 6) on the distribution of the electric �eld at the sur-face of the conductor and the possibility of initiating PD.The following parameters are determined in Fig. 7: E(x)� electric �eld distribution in SF6 gas between the con-ductor and grounded tank, Ed(x) � electric �eld distri-bution in the vicinity of defect on the conductor surface.Local increase of electric �eld in the vicinity of micro-

needle on the high voltage conductor (Fig. 7) is describedby the coe�cient βr = Erd/Er (where Erd � the high-est value of electric �eld at micro-needle defect; Er �maximal value of electric �eld at the conductor surface).

322 B. Florkowska, P. Zydro«, A. Jackowicz-Korczy«ski

The value of βr depends on the radius of defect curva-ture rd, while its shape has no essential meaning.

Fig. 7. Model of coaxial cylinders: (a) defect with ra-dius rd on high voltage conductor, (b) electric �eld dis-tribution in the vicinity of conductor E(x) and at thetip of the micro-needle defect Ed(x).

Amodel of micro-needle defect has been adopted as hy-perboloidal electrode in above-mentioned case [20]. Herethe electric �eld stress at a distance x from the needletip equals to

E (x) =2U

(2x+ rd − x2/a) ln(4a/rd). (5)

for 0 ≤ x ≤ (R − rd), where U � voltage betweenthe needle and grounded plane electrode, a � distance(a = R− r).Electric �eld stress at the point x = 0 is expressed by

equation

Erd =2U

rdln(4a/rd). (6)

Relations Ed(x) evaluated for the assumed reference volt-age value U = 1 kV and for defect radius rd in the rangefrom 50 µm to 500 µm (Fig. 7) show to the existenceof a region at a distance to about 10−1 cm, i.e. zoneof ionisation and space charge near the needle electrode(Fig. 8). The region at a distance greater than about 1 cmdoes not in�uence the distribution of electric �eld in thevicinity of the needle of di�erent curvature.The electric �eld distribution in the vicinity of the

needle-type defect on the conductor surface has beenmodelled on the basis of the following assumptions:

� height of defect h equals to 1, 3, or 5 mm,

� curvature radius rd equals to 50, 100, or 200 µm.

In a typical substation with the rated voltage of 340 kV,the radius of high voltage conductor is r = 55 mm and

Fig. 8. The electric �eld values in the distance of xfrom needle with di�erent curvatures rd from 50 µmto 500 µm (calculated for U = 1 kV).

the radius of outer electrode (metallic enclosure of GISmodule) is R = 152 mm. Exemplary result of numeri-cal simulation of the electric �eld spatial distribution inthe vicinity of the needle defect located on high voltageconductor is presented in Fig. 9.

Fig. 9. Example of electric �eld stress distribution inthe vicinity of the needle defect on the HV conductor inthe coaxial cylinders.

Fig. 10. Images of electric �eld in the vicinity of de-fects on the conductor (rd = 100 µm) for di�erent heightof defects: a) h = 1 mm, b) h = 5 mm.

Patterns of electric �eld stress presented in Fig. 10illustrate two selected cases when the electric �eldstress Erd does not excess the critical value, at which par-tial discharges can occur (defect: height h = 1 mm, rd =100 µm) (Fig. 10a), and when it goes beyond this value

Electric Field Modelling in Gas-Insulated Substation. . . 323

because of the higher needle-type defect (h = 5 mm,rd = 100 µm) (Fig. 10b).

4. Mechanism of partial discharges in SF6

Analysing the phenomena of partial discharges initi-ation and development in GIS one should take into ac-count the construction of the object and other physicalconditions, which are

� de�ned electrode con�guration,

� defect kind as the source of partial discharges, withdi�erent conditions of discharges initiation,

� possibilities of avalanche and streamer dischargesdevelopment,

� pulse form of these phenomena.

The discharge pulse consists of streamers propagatinginto gas from the tip of the micro-defect to a limited dis-tance in which the local electric �eld is equal or higherthan a critical value Ecr. This value in SF6 is relatedto the pressure of gas [21]. When E ≥ Ecr criterion isful�lled, the mechanism of PD initiation depends on thepolarity of the micro-needle:

� at the positive polarity � electrons are producedby the �eld detachment from negative ions,

� at negative polarity � the dominant phenomenonis the �eld emission from the metallic surface of thedefects.

Conducting particles located on insulator surface or inthe �triple point� enable the evolution of surface dis-charges. On the other hand, inner inclusions in insulatorsare the cause of inner erosion and evolution of treeing dis-charges.

4.1. Initiation of partial discharges from micro-needles

In the case of micro-needles on the surface of a con-ductor (Figs. 6 and 7) the conditions for discharges ini-tiation stem from the �eld emission and tunnel e�ect atthe micro-needle. The probability of �eld emission on theconductor/gas interface depends on the value of electric�eld stress Ed, at the surface of micro-needle (Fig. 11).The increase of electric �eld stress at the needle in re-lation to the average electric �eld stress (E = U/a) isexpressed by the coe�cient β = Ed/E. The current ef-�ciency of the �eld emission depends on the followingfactors:

� local electric �eld stress at the micro-needle Ed,

� electric �eld stress in the insulating system E,

� e�ective work of electron emission from metal ex-pressed by the Fowler�Nordheim formula [22]:

NeFN = πr2A1β2E2

Φefexp

−A2Φ3/2

efβE

, (7)

where Φef � e�ective work of electron emission fromcathode [eV], A1, A2 � constants: A1 = 1.54 ×10−6 eV A V−2, A2 = 6.79× 109 (eV)−3/2 V m−1.

Fig. 11. Model of a micro-needle on the conductor sur-face (CS).

The tunnel e�ect is most intense at the top of themicro-needle, but the height of the micro-needle shouldbe so determined as to make this e�ect appear. It is con-nected with the shape and width of the potential bar-rier at the metal surface as they are needed to evolvethis e�ect. The value of electron emission work Φef de-pends on the stage of micro-needle surface, particularlyon the presence of adsorbed atoms of other elementswhich can lower it or rise and also on the kind of in-terfaces, e.g. metal/gas, metal/solid dielectric. Above-mentioned problems are of particular meaning for the ini-tiation of discharges in vacuum insulating systems. Thusthe condition of discharges initiation due to �eld emissionresults from the relation NeFN = f(βE). Formula (7)indicates a strong dependence of �eld emission on theproduct βE so that for βE < (βE)∗ emission practicallydoes not exist and for βE > (βE)∗ it is intensive, while(βE)∗ is the threshold value between the initial and in-tensive emission. To evaluate the threshold value (βE)∗one should account for the emission of only one electronduring one half-period T of AC voltage, i.e. NeFN = 2e/T(e is the elementary charge). Then

(βE) ∗ =A2Φ

3/2

ef

ln

(A1πr2 T

2e[(βE)∗]2

Φef

) . (8)

Basing on the assumption that the work functions Φef

of electrons from metal stays in the range 3 ÷ 5 eV formicro-needles in vacuum, and 0.9 ÷ 1.5 eV for micro-needles in solid dielectric, time T/2 = 10 ms, and thetop surface of the micro-needle is 0.1 mm2 to 1 mm2,two relationships (βE)∗ = f(Φef) and Ed = f(Φef) havebeen worked out (Fig. 12) [18]. Threshold values of (βE)∗range from 6×108 V m−1 to 15×108 V m−1 � for micro-needle in gas, and from 1× 108 V m−1 to 3× 108 V m−1

� for micro-needle in solid dielectric, respectively.

324 B. Florkowska, P. Zydro«, A. Jackowicz-Korczy«ski

Fig. 12. Dependence of threshold value (βE)∗ and theelectric �eld stress E on the work of electron emissionfrom metal for surfaces 0.1 mm2 and 1 mm2.

If the coe�cient of micro-geometry is equal to, e.g.β = 100, then the values of electric �eld stress rangefrom 6 × 106 V m−1 to 15 × 106 V m−1 (i.e., 6 kV/mmto 15 kV/mm), and from 1×106 V m−1 to 3×106 V m−1

(i.e., 1 kV/mm to 3 kV/mm). These are values of workingelectric �eld stress in insulating systems.

4.2. Discharges development

Space development of electron avalanches in gas de-pends on impact ionisation processes characterised by co-e�cient α, and in the case of electronegative gases as SF6,also by electron attachment coe�cient η, which in�uencesthe number of electrons in an avalanche. The capture ofelectrons in SF6, when η 6= 0 results in the fact that theavalanche development is possible only for α > η.Further development of discharge in the form of

streamers in the limited space in gas above the top ofmicro-needle is connected with the self-propagation ofelectron avalanches as a result of �eld increase in the re-gion of space charge ionisation. Local �eld stress is thengreater than the critical value Ecr. On the other hand,this value depends on gas pressure. The development ofelectron avalanches is possible when

(E/p) > (E/p)cr. (9)

In electrodes with homogeneous or semi-homogeneous�eld in sulphur hexa�uoride the value (E/p)cr in the tem-perature 300 K equals to 89 V m−1 Pa−1 [21]. The pos-sible deformation of local electric �eld distribution andthe overvoltages in exploitation in view, the electric �eldstress on the HV conductor surface can be assumed notto exceed 8.9 V m−1 Pa−1 [23]. If the gas pressure in thesubstation is 0.5 MPa, electric �eld stress at the HV con-ductor equals to 4.5 kV/mm. The direction and area ofthe streamer discharge propagation depend on the kindof defect in the substation.In the case of micro-needle defects located on the

conducting elements the three-dimensional space of dis-charges in gas can be approximately modelled as the con-ducting sphere which cumulates the discharge charge.When the defects are conducting particles adherent to

the insulator surface, then it is approximately a two-dimensional area on the insulator surface which cumu-lates the charge. Di�erent kinds of discharge are pro-duced as the e�ect of discharges initiated by above men-tioned defects: in the �rst case they could be similar tocorona discharge, in the second � similar to the surfaceones.

5. Final remarks

Partial discharges in gas insulated substations mayexist because of di�erent imperfections (micro-needles,free particles, contaminations) in the substation mod-ules. Discharges are generated when the critical valueof electric �eld is achieved at any point located insidethe gaseous HV insulating system. Computer simulationof micro-needle model defects by means of �nite elementmethod is a tool for determining conditions for partialdischarges initiation when su�ciently high electric �eldis reached. It was shown during modelling that such ametallic defect on a high voltage conductor, working atde�ned voltage, could be a local source of partial dis-charges when it has speci�c geometrical dimensions.

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